Volume 1, Issue 2, August 2016, Page: 20-25
Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method
Hiqmet Kamberaj, Faculty of Engineering, Department of Computer Engineering, International Balkan University, Skopje, R. of Macedonia
Received: Jun. 15, 2015;       Accepted: Jul. 1, 2015;       Published: Jul. 16, 2016
DOI: 10.11648/j.eas.20160102.12      View  4168      Downloads  103
Abstract
We present a newly developed Replica Exchange algorithm using q -Gaussian Swarm Quantum Particle Optimization (REX@q-GSQPO) method for solving the problem of finding the global optimum. The basis of the algorithm is to run multiple copies of independent swarms at different values of q parameter. Based on an energy criterion, chosen to satisfy the detailed balance, we are swapping the particle coordinates of neighboring swarms at regular iteration intervals. The swarm replicas with high q values are characterized by high diversity of particles allowing escaping local minima faster, while the low q replicas, characterized by low diversity of particles, are used to sample more efficiently the local basins. We compared the new algorithm with the standard Gaussian Swarm Quantum Particle Optimization (GSQPO) and q-Gaussian Swarm Quantum Particle Optimization (q-GSQPO) algorithms, and found that the new algorithm is more robust in terms of the number of fitness function calls, and more efficient in terms of ability to convergence faster to the global minimum. In additional, we also provide a method for optimally allocating the swarm replicas among different q values. Our algorithm is tested for three benchmark functions, which are known to be multimodal problems, at different dimensionalities.
Keywords
Swarm Quantum Particle, q-Gaussian Distribution, Global Optimization, Replica Exchange
To cite this article
Hiqmet Kamberaj, Replica Exchange Using q-Gaussian Swarm Quantum Particle Intelligence Method, Engineering and Applied Sciences. Vol. 1, No. 2, 2016, pp. 20-25. doi: 10.11648/j.eas.20160102.12
Reference
[1]
O. Becker and M. Karplus, J. Chem. Phys. 106 (1997) 1495-1517.
[2]
D. Wales, Energy Landscapes with applications to clusters, biomolecules and glasses, Cambridge University Press, Cambridge, UK, 2003.
[3]
H. Schmeck and J. Branke, Designing evolutionary algorithms for dynamic optimization problems. Theory and application of evoluacionary computation: recent trends, S. Tsutsui and A. Ghosh, Eds., (2002) 239-262.
[4]
J. Kennedy, R. Eberhart and Y. Shi, Swarm Intelligence, Morgan Kaufmann, Los Altos, CA, 2001.
[5]
K. Parsopoulos and M. Vrahatis, Natural Computing, (2002) 235-306.
[6]
A. Walczak, W. Bialek, A. Cavagna, I. Giardina, T. Mora, E. Silvestri and M. Viale, Proc. Natl. Acad. Sci. USA. 109 (2012) 4786-4791.
[7]
T. Blackwell, R. Poli and J. Kennedy, Swarm Intell. 1 (2007) 33–57.
[8]
J. Kennedy, In Proceedings of the 2007 IEEE Swarm Intelligence Symposium, Honolulu, HI, 2007, pp. 162-169.
[9]
M. Clerc and J. Kennedy, Evolutionary Computation, IEEE Transactions on Evolutionary Computation 6 (2002) 58-73.
[10]
A. Banks, J. Vincent and C. Anyakoha, Natural Computing 6 (2007) 467-484.
[11]
A. Banks, J. Vincent and C. Anyakoha, Natural Computing 7 (2008) 109-124.
[12]
J. Sun, B. Feng and W. Xu, In the Proceedings of the 2004 IEEE congress on evolutionary computation, Piscataway, NJ, 2004, pp. 325-331.
[13]
J. Sun, B. Feng and W. Xu, In Proceedings of the 2004 IEEE conference on Cybernetics and Intelligent Systems, Singapore, 2004, pp. 111-116.
[14]
S. Mikki and A. Kishk, IEEE Trans. Antenn. Propag. 54 (2006) 2764–2775.
[15]
W. Xu, J. Liu and J. Sun, Quantum-behaved particle swarm optimization with adaptive mutation operator, Part I, Springer-Verlag, 2006.
[16]
W. Fang, J. Sun, Y. Ding, X. Wu and W. Xu, IETE Technical Review 27 (2010) 337-348.
[17]
J. Liu, J. Sun and W. Xu, Advances in Natural Computation 3612 (2005) 543-552.
[18]
J. Sun, W. Xu and B. Feng, In Proceedings of the 2005 IEEE International Conference on Systems, Man and Cybernetics, Waikoloa, HI, 2005, pp. 3049-3054.
[19]
J. Sun, W. Xu and W. Fang, In Proceedings of the 2006 Simulated Evolution and Learning Hefei, China, 2006, pp. 497-504.
[20]
J. Sun, W. Xu and W. Fang, In Proceedings of the 2006 Rough Sets and Current Trends in Computing, Kobe, Japan, 2006, pp. 736-745.
[21]
J. Sun, W. Xu and W. Fang, In Proceedings of the 2006 International Conference on Computational Science, Springer, Berlin, Heidelberg, 2006, pp. 847-854.
[22]
W. Xu, M. Xi and J. Sun, Appl. Math. Comput. 205 (2008) 751-759.
[23]
W. Xu, W. Fang, J. Sun, Y. Ding and X. Wu, IETE Technical Review 27 (2010) 336-348.
[24]
H. Kamberaj, Appl. Math. Comput. 229 (2014) 94-106.
[25]
J. Straub and I. Andricioaei, Brazilian J. Phys. 29 (1999) 179-186.
[26]
D. Stariolo and C. Tsallis, Annual Reviews of Computational Physics II, editied by D. Stauffer, Singapore, World Scientific, 1995.
[27]
H. Kamberaj and A. van der Vaart, J. Chem. Phys. 127 (2007) 234102-7.
[28]
C. Tsallis and D. Stariolo, Physica A 233 (1996) 395-406.
[29]
S. Umarov, C. Tsallis and S. Steinberg, Milan J. Math. 76 (2008) 307-328.
[30]
C. Tsallis, J. Stat. Phys. 52 (1988) 479-487.
[31]
I. Andricioaei and J. Straub, J. Chem. Phys. 107 (1997) 9117-9125.
[32]
J. Riget and J. Vesterstroem, A diversity-guided particle swarm optimizer - the ARPSO, Department of Computer Science, University of Aarhus, 2002.
[33]
K. Hukushima and K. Nemoto, J. Phys. Soc. (Jpn) 65 (1996) 1604-1607.
[34]
R. H. Swendsen and J.-S. Wang, Phys. Rev. Lett. 58 (1987) 86-88.
[35]
Y. Okamoto and Y. Sugita, Chem. Phys. Lett. 314 (1999) 141-151.
[36]
H. Kamberaj and A. van der Vaart, J. Chem. Phys. 130 (2009) 074906.
[37]
H. Fukunishi, O. Watanabe and S. Takada, J. Chem. Phys. 116 (2002) 9058-9068.
[38]
J. Kim and J. Straub, J. Chem. Phys. 130 (2009) 144114-11.
[39]
D. Ackley, A connectionist machine for genetic hillclimbing, Kluwer Academic Publishers, Boston, 1987.
[40]
A. Griewank, J. Optimiz. Theory App. 34 (1981) 11-39.
[41]
P. Angeline, Evolutionary Optimization Versus Particle Swarm Optimization: Philosophy and Performance Differences, Evolutionary Programming VII, Lecture Notes in Computer Science, Springer, Berlin, Heidelberg, New York, 1998.
[42]
L. Meester, F. Dekking, C. Kraaikamp and H. Lopuhaa, A Modern Introduction to Probability and Statistics, Springer-Verlag, London, 2005.
[43]
H. Kamberaj, Cent. Eur. J. Phys. 9 (2011) 96-109.
[44]
X. Zhao, W. Lin and Q. Zhang, Appl. Math. Comput. 229 (2014) 440-456.
Browse journals by subject